Building upon score-based learning, new interest in stochastic localization
techniques has recently emerged. In these models, one seeks to noise a sample
from the data distribution through a stochastic process, called observation
process, and progressively learns a denoiser associated to this dynamics. Apart
from specific applications, the use of stochastic localization for the problem
of sampling from an unnormalized target density has not been explored
extensively. This work contributes to fill this gap. We consider a general
stochastic localization framework and introduce an explicit class of
observation processes, associated with flexible denoising schedules. We provide
a complete methodology, $\textit{Stochastic Localization via Iterative
Posterior Sampling}$ (SLIPS), to obtain approximate samples of this dynamics,
and as a by-product, samples from the target distribution. Our scheme is based
on a Markov chain Monte Carlo estimation of the denoiser and comes with
detailed practical guidelines. We illustrate the benefits and applicability of
SLIPS on several benchmarks, including Gaussian mixtures in increasing
dimensions, Bayesian logistic regression and a high-dimensional field system
from statistical-mechanics.

通过引入一种称为观测过程的随机过程，从数据分布中随机噪声样本并逐步学习与此动力学相关联的去噪器，本文在基于分数的学习的基础上，对随机定位技术产生了兴趣。除了特定的应用外，使用随机定位来从未归一化的目标密度中采样的问题尚未广泛探讨。本文填补了这个空白。我们考虑了一个广义的随机定位框架，并引入了一类明确的观测过程，与灵活的去噪时间表相关联。我们提供了一个完整的方法，即 “通过迭代后验采样进行随机定位”（SLIPS），以获取此动态的近似样本，并作为副产品获得目标分布的样本。我们的方案基于马尔可夫链蒙特卡洛估计的去噪器，并带有详细的实际指南。我们以几个基准测试为例，包括维度逐渐增加的高斯混合模型、贝叶斯逻辑回归和高维统计力学场系统，以证明 SLIPS 的益处和适用性。

通过迭代后验抽样进行随机定位

Stochastic Localization via Iterative Posterior Sampling

Diffusions are a successful technique to sample from high-dimensional
distributions can be either explicitly given or learnt from a collection of
samples. They implement a diffusion process whose endpoint is a sample from the
target distribution and whose drift is typically represented as a neural
network. Stochastic localization is a successful technique to prove mixing of
Markov Chains and other functional inequalities in high dimension. An
algorithmic version of stochastic localization was introduced in [EAMS2022], to
obtain an algorithm that samples from certain statistical mechanics models.
This notes have three objectives: (i) Generalize the construction [EAMS2022]
to other stochastic localization processes; (ii) Clarify the connection between
diffusions and stochastic localization. In particular we show that standard
denoising diffusions are stochastic localizations but other examples that are
naturally suggested by the proposed viewpoint; (iii) Describe some insights
that follow from this viewpoint.

通过扩展随机本地化过程并澄清扩散过程与随机本地化之间的联系，本文提出实现从高维分布中采样的有效技术，其中扩散过程的漂移通常表示为神经网络，并使用相应的算法从某些统计力学模型中采样。